Bayes Optimal Estimation and Its Approximation Algorithm for Difference with and without Treatment under URLC Model

In this paper, we propose the data generative model in which a target population is divided into several latent classes, and the probability distribution of responses within each latent class is the same under a given treatment. We call this model the Uniform Response Latent Class model (URLC model). Under the proposed model, we calculate Bayesian optimal decision and its approximation algorithm for the difference with and without the treatment for the entire population. We conduct experiments and confirm the following characteristics of the proposed algorithm: 1) our algorithm correctly estimates the true number of latent classes even if the number of latent classes is not known. 2) given the synthetic data generated from the proposed model, the mean square error is smaller than the conventional method. 3) when the class tendency is different, the mean square error is smaller than the conventional method. 4) given the synthetic data from SEM, our propose method works well.